SOLUTION: Hi the question is: The graphs of the equations -x+2y=6, 7x+y=3, and 2x+y=8 contain the sides of a triangle. Find the coordinates of the vertices of the triangle. I already graphed

Question 191328This question is from textbook Algebra 1
: Hi the question is: The graphs of the equations -x+2y=6, 7x+y=3, and 2x+y=8 contain the sides of a triangle. Find the coordinates of the vertices of the triangle. I already graphed the lines, but I do not know how to find the vertices of the triangle. Thank You! This question is from textbook Algebra 1

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The graphs of the equations -x+2y=6, 7x+y=3, and 2x+y=8 contain the sides of a triangle. Find the coordinates of the vertices of the triangle. I already graphed the lines, but I do not know how to find the vertices of the triangle.
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From the graph, they appear to be (0,3), (2,4) and (-1,10).
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To find them exactly, take the eqns 2 at a time and solve for x and y.
-x+2y = 6 --> x = 2y - 6
7x + y = 3
Sub for x into 2nd eqn
7*(2y-6) + y = 3
14y-42 + y = 3
15y = 45
y = 3
x = 0
So one point is (0,3)
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-x+2y = 6 --> x = 2y - 6
2x+y=8
Sub for x again
2(2y-6) + y = 8
4y-12 + y = 8
y = 4
x = 2
(2,4) is a vertex
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You can do the 3rd one. if you have questions or want me to check your work, email me via the thank you note.

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